ITP001 Axioms: ITP131_5.ax
%------------------------------------------------------------------------------
% File : ITP131_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : powser_2.ax [Gau20]
% : HL4131_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 74 ( 13 unt; 29 typ; 0 def)
% Number of atoms : 1268 ( 39 equ)
% Maximal formula atoms : 8 ( 17 avg)
% Number of connectives : 55 ( 2 ~; 0 |; 12 &)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1170 (1170 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 60 ( 28 >; 32 *; 0 +; 0 <<)
% Number of predicates : 36 ( 35 usr; 27 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 1 con; 0-4 aty)
% Number of variables : 135 ( 135 !; 0 ?; 135 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Epowser_2Ediffs,type,
c_2Epowser_2Ediffs: $i ).
tff(mem_c_2Epowser_2Ediffs,axiom,
mem(c_2Epowser_2Ediffs,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) ).
tff(lamtp_f2842,type,
f2842: ( tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2842,axiom,
! [V2y: tp__ty_2Erealax_2Ereal,V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V3p: tp__ty_2Enum_2Enum] : ( ap(f2842(V2y,V0n,V1x),inj__ty_2Enum_2Enum(V3p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V3p))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V3p)))) ) ).
tff(lamtp_f2843,type,
f2843: ( tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2843,axiom,
! [V2y: tp__ty_2Erealax_2Ereal,V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V4p: tp__ty_2Enum_2Enum] : ( ap(f2843(V2y,V0n,V1x),inj__ty_2Enum_2Enum(V4p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V4p))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V4p)))) ) ).
tff(conj_thm_2Epowser_2EPOWDIFF__LEMMA,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),f2842(V2y,V0n,V1x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V2y)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),f2843(V2y,V0n,V1x)))) ) ).
tff(lamtp_f2844,type,
f2844: ( tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2844,axiom,
! [V2y: tp__ty_2Erealax_2Ereal,V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V3p: tp__ty_2Enum_2Enum] : ( ap(f2844(V2y,V0n,V1x),inj__ty_2Enum_2Enum(V3p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V3p))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V3p)))) ) ).
tff(conj_thm_2Epowser_2EPOWDIFF,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V2y))),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),f2844(V2y,V0n,V1x)))) ) ).
tff(lamtp_f2845,type,
f2845: ( tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2845,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V4p: tp__ty_2Enum_2Enum] : ( ap(f2845(V0n,V1x,V2y),inj__ty_2Enum_2Enum(V4p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V4p)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2y)),inj__ty_2Enum_2Enum(V4p))) ) ).
tff(conj_thm_2Epowser_2EPOWREV,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),f2844(V2y,V0n,V1x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))),f2845(V0n,V1x,V2y))) ) ).
tff(lamtp_f2846,type,
f2846: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2846,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V3n: tp__ty_2Enum_2Enum] : ( ap(f2846(V0f,V1x),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V3n))) ) ) ).
tff(lamtp_f2847,type,
f2847: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2847,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2z: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ( ap(f2847(V0f,V2z),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Eabs,ap(V0f,inj__ty_2Enum_2Enum(V4n)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Epowser_2EPOWSER__INSIDEA,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(c_2Eseq_2Esummable,f2846(V0f,V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2z))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x)))) )
=> p(ap(c_2Eseq_2Esummable,f2847(V0f,V2z))) ) ) ).
tff(lamtp_f2848,type,
f2848: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2848,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2z: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ( ap(f2848(V0f,V2z),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2z)),inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Epowser_2EPOWSER__INSIDE,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
( ( p(ap(c_2Eseq_2Esummable,f2846(V0f,V1x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2z))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x)))) )
=> p(ap(c_2Eseq_2Esummable,f2848(V0f,V2z))) ) ) ).
tff(lamtp_f2849,type,
f2849: $i > $i ).
tff(lameq_f2849,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum] : ( ap(f2849(V0c),inj__ty_2Enum_2Enum(V1n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))),ap(V0c,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))) ) ) ).
tff(ax_thm_2Epowser_2Ediffs,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( ap(c_2Epowser_2Ediffs,V0c) = f2849(V0c) ) ) ).
tff(lamtp_f2850,type,
f2850: $i > $i ).
tff(lameq_f2850,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1n: tp__ty_2Enum_2Enum] : ( ap(f2850(V0c),inj__ty_2Enum_2Enum(V1n)) = ap(c_2Erealax_2Ereal__neg,ap(V0c,inj__ty_2Enum_2Enum(V1n))) ) ) ).
tff(lamtp_f2851,type,
f2851: $i > $i ).
tff(lameq_f2851,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(f2851(V0c),inj__ty_2Enum_2Enum(V2n)) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Epowser_2Ediffs,V0c),inj__ty_2Enum_2Enum(V2n))) ) ) ).
tff(conj_thm_2Epowser_2EDIFFS__NEG,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ( ap(c_2Epowser_2Ediffs,f2850(V0c)) = f2851(V0c) ) ) ).
tff(lamtp_f2852,type,
f2852: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2852,axiom,
! [V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3n: tp__ty_2Enum_2Enum] : ( ap(f2852(V1c,V2x),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V1c),inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V3n))) ) ) ).
tff(lamtp_f2853,type,
f2853: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2853,axiom,
! [V2x: tp__ty_2Erealax_2Ereal,V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V4n: tp__ty_2Enum_2Enum] : ( ap(f2853(V2x,V1c),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Erealax_2Ereal__mul,ap(V1c,inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V4n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ) ).
tff(conj_thm_2Epowser_2EDIFFS__LEMMA,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2852(V1c,V2x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2853(V2x,V1c))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Erealax_2Ereal__mul,ap(V1c,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))) ) ) ).
tff(lamtp_f2854,type,
f2854: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2854,axiom,
! [V2x: tp__ty_2Erealax_2Ereal,V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n: tp__ty_2Enum_2Enum] : ( ap(f2854(V2x,V1c),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Erealax_2Ereal__mul,ap(V1c,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ) ).
tff(lamtp_f2855,type,
f2855: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2855,axiom,
! [V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ( ap(f2855(V1c,V2x),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V1c),inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Epowser_2EDIFFS__LEMMA2,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
( mem(V1c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2854(V2x,V1c))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))),f2855(V1c,V2x))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Erealax_2Ereal__mul,ap(V1c,inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))) ) ) ).
tff(lamtp_f2856,type,
f2856: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2856,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] : ( ap(f2856(V0c,V1x),inj__ty_2Enum_2Enum(V2n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V0c),inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V2n))) ) ) ).
tff(lamtp_f2857,type,
f2857: ( tp__ty_2Erealax_2Ereal * $i ) > $i ).
tff(lameq_f2857,axiom,
! [V1x: tp__ty_2Erealax_2Ereal,V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V3n: tp__ty_2Enum_2Enum] : ( ap(f2857(V1x,V0c),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Erealax_2Ereal__mul,ap(V0c,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) ) ) ).
tff(lamtp_f2858,type,
f2858: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2858,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ( ap(f2858(V0c,V1x),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V0c),inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(conj_thm_2Epowser_2EDIFFS__EQUIV,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(c_2Eseq_2Esummable,f2856(V0c,V1x)))
=> p(ap(ap(c_2Eseq_2Esums,f2857(V1x,V0c)),ap(c_2Eseq_2Esuminf,f2858(V0c,V1x)))) ) ) ).
tff(lamtp_f2859,type,
f2859: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2859,axiom,
! [V2h: tp__ty_2Erealax_2Ereal,V1z: tp__ty_2Erealax_2Ereal,V0m: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum] : ( ap(f2859(V2h,V1z,V0m),inj__ty_2Enum_2Enum(V3p)) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V2h))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V3p)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Enum_2Enum(V3p)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Enum_2Enum(V0m))) ) ).
tff(lamtp_f2860,type,
f2860: ( tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2860,axiom,
! [V0m: tp__ty_2Enum_2Enum,V2h: tp__ty_2Erealax_2Ereal,V1z: tp__ty_2Erealax_2Ereal,V4p: tp__ty_2Enum_2Enum] : ( ap(f2860(V0m,V2h,V1z),inj__ty_2Enum_2Enum(V4p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Enum_2Enum(V4p))),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V2h))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V4p)))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1z)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V4p))))) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF__LEMMA1,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1z: tp__ty_2Erealax_2Ereal,V2h: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0m))),f2859(V2h,V1z,V0m))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0m))),f2860(V0m,V2h,V1z))) ) ).
tff(lamtp_f2861,type,
f2861: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2861,axiom,
! [V2n: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum,V1h: tp__ty_2Erealax_2Ereal,V0z: tp__ty_2Erealax_2Ereal,V4q: tp__ty_2Enum_2Enum] : ( ap(f2861(V2n,V3p,V1h,V0z),inj__ty_2Enum_2Enum(V4q)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1h))),inj__ty_2Enum_2Enum(V4q))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V3p))),inj__ty_2Enum_2Enum(V4q)))) ) ).
tff(lamtp_f2862,type,
f2862: ( tp__ty_2Enum_2Enum * tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2862,axiom,
! [V2n: tp__ty_2Enum_2Enum,V1h: tp__ty_2Erealax_2Ereal,V0z: tp__ty_2Erealax_2Ereal,V3p: tp__ty_2Enum_2Enum] : ( ap(f2862(V2n,V1h,V0z),inj__ty_2Enum_2Enum(V3p)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V3p))),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V3p)))),f2861(V2n,V3p,V1h,V0z))) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF__LEMMA2,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1h: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum] :
( ( V1h != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1h))),inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V2n)))),inj__ty_2Erealax_2Ereal(V1h))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1h)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),f2862(V2n,V1h,V0z)))) ) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF__LEMMA3,axiom,
! [V0z: tp__ty_2Erealax_2Ereal,V1h: tp__ty_2Erealax_2Ereal,V2n: tp__ty_2Enum_2Enum,V3k_27: tp__ty_2Erealax_2Ereal] :
( ( ( V1h != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0z))),inj__ty_2Erealax_2Ereal(V3k_27)))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1h)))),inj__ty_2Erealax_2Ereal(V3k_27))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1h))),inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V2n)))),inj__ty_2Erealax_2Ereal(V1h))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V3k_27)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1h))))))) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF__LEMMA4,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ! [V1k_27: tp__ty_2Erealax_2Ereal,V2k: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2k)))
& ! [V3h: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))),inj__ty_2Erealax_2Ereal(V2k))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(V0f,inj__ty_2Erealax_2Ereal(V3h)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1k_27)),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))))) ) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,V0f),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ).
tff(lamtp_f2863,type,
f2863: $i > $i ).
tff(lameq_f2863,axiom,
! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)))
=> ! [V5h: tp__ty_2Erealax_2Ereal] : ( ap(f2863(V1g),inj__ty_2Erealax_2Ereal(V5h)) = ap(c_2Eseq_2Esuminf,ap(V1g,inj__ty_2Erealax_2Ereal(V5h))) ) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF__LEMMA5,axiom,
! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)))
=> ! [V2k: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2k)))
& p(ap(c_2Eseq_2Esummable,V0f))
& ! [V3h: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))),inj__ty_2Erealax_2Ereal(V2k))) )
=> ! [V4n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(V1g,inj__ty_2Erealax_2Ereal(V3h)),inj__ty_2Enum_2Enum(V4n)))),ap(ap(c_2Erealax_2Ereal__mul,ap(V0f,inj__ty_2Enum_2Enum(V4n))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V3h))))) ) )
=> p(ap(ap(ap(c_2Elim_2Etends__real__real,f2863(V1g)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ) ).
tff(lamtp_f2864,type,
f2864: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2864,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1k_27: tp__ty_2Erealax_2Ereal,V3n: tp__ty_2Enum_2Enum] : ( ap(f2864(V0c,V1k_27),inj__ty_2Enum_2Enum(V3n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0c,inj__ty_2Enum_2Enum(V3n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1k_27)),inj__ty_2Enum_2Enum(V3n))) ) ) ).
tff(lamtp_f2865,type,
f2865: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2865,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1k_27: tp__ty_2Erealax_2Ereal,V4n: tp__ty_2Enum_2Enum] : ( ap(f2865(V0c,V1k_27),inj__ty_2Enum_2Enum(V4n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V0c),inj__ty_2Enum_2Enum(V4n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1k_27)),inj__ty_2Enum_2Enum(V4n))) ) ) ).
tff(lamtp_f2866,type,
f2866: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2866,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1k_27: tp__ty_2Erealax_2Ereal,V5n: tp__ty_2Enum_2Enum] : ( ap(f2866(V0c,V1k_27),inj__ty_2Enum_2Enum(V5n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,ap(c_2Epowser_2Ediffs,V0c)),inj__ty_2Enum_2Enum(V5n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1k_27)),inj__ty_2Enum_2Enum(V5n))) ) ) ).
tff(lamtp_f2867,type,
f2867: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2867,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V6x: tp__ty_2Erealax_2Ereal,V7n: tp__ty_2Enum_2Enum] : ( ap(f2867(V0c,V6x),inj__ty_2Enum_2Enum(V7n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(V0c,inj__ty_2Enum_2Enum(V7n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Enum_2Enum(V7n))) ) ) ).
tff(lamtp_f2868,type,
f2868: $i > $i ).
tff(lameq_f2868,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V6x: tp__ty_2Erealax_2Ereal] : ( ap(f2868(V0c),inj__ty_2Erealax_2Ereal(V6x)) = ap(c_2Eseq_2Esuminf,f2867(V0c,V6x)) ) ) ).
tff(lamtp_f2869,type,
f2869: ( $i * tp__ty_2Erealax_2Ereal ) > $i ).
tff(lameq_f2869,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V2x: tp__ty_2Erealax_2Ereal,V8n: tp__ty_2Enum_2Enum] : ( ap(f2869(V0c,V2x),inj__ty_2Enum_2Enum(V8n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Epowser_2Ediffs,V0c),inj__ty_2Enum_2Enum(V8n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Enum_2Enum(V8n))) ) ) ).
tff(conj_thm_2Epowser_2ETERMDIFF,axiom,
! [V0c: $i] :
( mem(V0c,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
=> ! [V1k_27: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
( ( p(ap(c_2Eseq_2Esummable,f2864(V0c,V1k_27)))
& p(ap(c_2Eseq_2Esummable,f2865(V0c,V1k_27)))
& p(ap(c_2Eseq_2Esummable,f2866(V0c,V1k_27)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2x))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1k_27)))) )
=> p(ap(ap(ap(c_2Elim_2Ediffl,f2868(V0c)),ap(c_2Eseq_2Esuminf,f2869(V0c,V2x))),inj__ty_2Erealax_2Ereal(V2x))) ) ) ).
%------------------------------------------------------------------------------